# Planimetrics - math word problems

Study plane measurements, including angles, distances, and areas. In other words - measurement and calculation of shapes in the plane. Perimeter and area of plane shapes.

#### Number of problems found: 1947

• Cuboidal room Length of cuboidal room is 2m breadth of cuboidal room is 3m and height is 6m find the length of the longest rod that can be fitted in the room
• The diagonals The diagonals of the KOSA diamond are 20 cm and 48 cm long. Calculate the circumference of the diamond in centimeters rounded to one unit.
• Inscribed triangle To a circle is inscribed triangle so that the it's vertexes divide circle into 3 arcs. The length of the arcs are in the ratio 2:3:7. Determine the interior angles of a triangle.
• Regular hexagonal prism Calculate the volume of a regular hexagonal prism whose body diagonals are 24cm and 25cm long.
• Arm Calculate the length of the arm r of isosceles triangle ABC, with base |AB| = 14 cm and a height v=18 cm.
• 3x square The side length of the square is 54 cm. How many times increases the content area of a square if the length of side increase three times?
• Diagonal Calculate the diagonal length of the rectangle ABCD with sides a = 8 cm, b = 7 cm.
• Irregular pentagon A rectangle-shaped, 16 x 4 cm strip of paper is folded lengthwise so that the lower right corner is applied to the upper left corner. What area does the pentagon have?
• Concentric circles There is given a circle K with a radius r = 8 cm. How large must a radius have a smaller concentric circle that divides the circle K into two parts with the same area?
• Flowerbed In the park there is a large circular flowerbed with a diameter of 12 m. Jakub circulated him ten times and the smaller Vojtoseven times. How many meters each went by and how many meters did Jakub run more than Vojta?
• Centre of mass The vertices of triangle ABC are from the line p distances 3 cm, 4 cm and 8 cm. Calculate distance from the center of gravity of the triangle to line p.
• In a In a right triangle, the areas of the squares above its sides are 169; 25 and 144. The length of its longer leg is:
• Gardens The garden has the square shape with circumference 124 m. Divide it into two rectangular gardens, one should circumference 10 meters more than the second. What size will have a gardens?
• Triangle ABC Calculate the sides of triangle ABC with area 1404 cm2 and if a: b: c = 12:7:18
• Area of trapezoid The trapezoid bases are and 7 dm and 11 cm. His height is 4 cm. Calculate the area of the trapezoid.
• Diagonals of pentagon Calculate the diagonal length of the regular pentagon: a) inscribed in a circle of radius 12dm; b) a circumscribed circle with a radius of 12dm.
• Surface and volume Find the surface and volume of the rotating cone if the circumference of its base is 62.8 m and the side is 25 m long.
• Trapezium The area of trapezium is 35cm2 find its altitude if the bases are 6cm and 8cm.
• Tunnel boring How much material did they dig when cutting the 400m long tunnel? The content of the circular segment, which is the cross section of the tunnel is 62m2.
• Rectangle Find the dimensions of the rectangle, whose perimeter is 108 cm and the length is 25% larger than the width.

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